Question

An insurance company found that 25% of all insurance policies are terminated before their maturity date. Assume that 10 polices are randomly selected from the company's policy database. Out of the 10 randomly selected policies;

a) What is the expected number of policies to be terminated before maturing? b) What is the standard deviation for the number of policies terminated before maturity? c) What is the probability that no policy will be terminated before maturity? d) What is the probability that all policies will be terminated before maturing? e) What is the probability that at least two policies will be terminated? f) What is the probability that more than 5 but less than eight policies will be terminated? g) What is the probability that at most eight policies will be terminated? h) What is the probability that eleven policies will be terminated? i) What is the probability that two policies will not be terminated?

QUESTION

Research has shown that 70% of new Small Medium Enterprises (SMEs) are started by graduates while 30% are started by non-graduates. It is also known that 60% of SMEs started by graduates are successful i.e. they survive beyond 3 years, while only 20% of those started by non-graduates are successful.

a) If it is known that a new SME has failed, what is the probability that it was started by a non-graduate? b) What is the probability that a new SME will be successful?

QUESTION

A short term insurance company receives seven motor vehicle claims, on average, per week. Assume that the daily claims follow a Poisson process and 7 working days per week.

a) What is the expected number of motor vehicle claims per month? b) What is the probability that on a given day no more than two motor vehicle claims will be received? c) What is the probability that more than three motor vehicle claims will be received over any given period of half a week i.e. 3.5 days? d) What is the probability that more than 6 but less than 10 motor vehicle claims will be received in any given week?

QUESTION

A courier service company has found that their delivery time of parcels to clients is approximately normally distributed with a mean delivery time of 50 minutes and a variance of 25 minutes (squared).

a) What is the probability that a randomly selected parcel will take 60 minutes to deliver? b) What is the probability that a randomly selected parcel will take between 38.75 and 55 minutes to deliver? c) What is the probability that a randomly selected parcel will take more than 36.25 minutes to deliver? d) What is the probability that a randomly selected parcel will take more than 59.25 minutes to deliver? e) What is the minimum delivery time for the 2.5% of parcels with the longest time to deliver?[4]